3 years ago

Completing the square when the equation doesn't equal 0, e.g.

Mathematics

1 answer:

Hunter-Best [27]3 years ago

3 0

It's as it is said $y = x^2+6x+12$ .
Your question is unclear.

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Let $f(x)$ be a function defined for all positive real numbers satisfying the conditions $f(x) > 0$ for all $x > 0$ and $f

algol [13]

Suppose we choose $x=1$ and $y=\dfrac12$ . Then

$f(x-y)=\sqrt{f(xy)+1}\implies f\left(\dfrac12\right)=\sqrt{f\left(\dfrac12\right)+1}\implies f\left(\dfrac12\right)=\dfrac{1+\sqrt5}2$

Now suppose we choose $x,y$ such that

$\begin{cases}x-y=\dfrac12\\\\xy=2009\end{cases}$

where we pick the solution for this system such that $x>y>0$ . Then we find

$\dfrac{1+\sqrt5}2=\sqrt{f(2009)+1}\implies f(2009)=\dfrac{1+\sqrt5}2$

Note that you can always find a solution to the system above that satisfies $x>y>0$ as long as $x>\dfrac12$ . What this means is that you can always find the value of $f(x)$ as a (constant) function of $f\left(\dfrac12\right)$ .

3 0

3 years ago

Read 2 more answers

Find the value of x in the triangle shown below. a. x=80 b. x=48 c. x= 32 d. x=12

yulyashka [42]

THEOREM:

• Pythagorean theorem:— In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

ANSWER:

By pythagorean property,

x² = 4² + 8²

x² = 16 + 64

x² = 80

x = √80 units.

So, Correct choice - [A] √80 units.

8 0

2 years ago

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A car dealer has 8 rows of cars with 16 cars in each. In each of the first 3 rows, 6 are used cars. The rest of the cars new car

qwelly [4]

The answer is 110 because if you multiply 8•16=128 and 18 cars are used, you subtract 128-18 which is 110.

8 0

3 years ago

Isabelle bought 12 bottles of water at $2 each

skad [1K]

$24, 2 Times 12 = 24

6 0

3 years ago

John bought an old motor bike for $ 5675 and spent $ 453 on its repair. Then he sold it in $ 7265, find out the profit he made.

drek231 [11]

Answer:

1137

Step-by-step explanation:

5675+453

6128

Now

7265-6128

1137

4 0

3 years ago